TY - JOUR
T1 - Bilinear estimates and applications to nonlinear wave equations
AU - Klainerman, Sergiu
AU - Selberg, Sigmund
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2002
Y1 - 2002
N2 - We undertake a systematic review of results proved in [26, 27, 30-32] concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we give a considerably simplified and unified treatment of these results and provide also complete proofs for large data. The paper is also intended as an introduction to and survey of current research in the very active area of nonlinear wave equations. The key ingredients throughout the survey are the use of the null structure of the equations we consider and, intimately tied to it, bilinear estimates.
AB - We undertake a systematic review of results proved in [26, 27, 30-32] concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we give a considerably simplified and unified treatment of these results and provide also complete proofs for large data. The paper is also intended as an introduction to and survey of current research in the very active area of nonlinear wave equations. The key ingredients throughout the survey are the use of the null structure of the equations we consider and, intimately tied to it, bilinear estimates.
UR - http://www.scopus.com/inward/record.url?scp=0036015432&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036015432&partnerID=8YFLogxK
U2 - 10.1142/S0219199702000634
DO - 10.1142/S0219199702000634
M3 - Article
AN - SCOPUS:0036015432
SN - 0219-1997
VL - 4
SP - 223
EP - 295
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 2
ER -